#### The observed infall of galaxies towards the Virgo cluster

I. D. Karachentsev
O. G. Nasonova
Special Astrophysical Observatory of the Russian Academy of Sciences
Nizhnij Arkhyz
KChR
Russia
A B S T R A C T We examine the velocity field of galaxies around the Virgo cluster induced by its overdensity. We have studied the velocity-distance relation in Virgocentric coordinates using a sample of 1792 galaxies with distances from the tip of the Red Giant Branch, the Cepheid luminosity, the luminosity of type Ia supernovae, the surface brightness fluctuation method and the TullyFisher relation. Attention was paid to some observational biases affecting the Hubble flow around Virgo. We estimate the radius of the zero-velocity surface for the Virgo cluster to be within 5.0-7.5 Mpc, corresponding to 17-26 at the mean cluster distance of 17.0 Mpc. In the case of spherical symmetry with the cosmological parameter m = 0.24 and the age of the Universe T 0 = 13.7 Gyr, it yields the total mass of the Virgo cluster to be within MT = (2.7-8.9) 1014 M in reasonable agreement with the existing virial mass estimates for the cluster.
1 I N T R O D U C T I O N
The gravitational action of the mass of a solitary system of galaxies
leads to deceleration of the local Hubble flow. As a result, the line
of average velocity of neighbouring galaxies relative to the centre
of a cluster (or a group) deviates from the linear Hubble relation,
going to negative values at small distances R < R0. Here, R0 denotes
the radius of the zero-velocity surface, which separates the galaxy
system against the global cosmic expansion. As shown by
LyndenBell (1981) and Sandage (1986), in the simplest case of spherical
symmetry with the cosmological parameter = 0 the radius R0
depends only on the total mass of a group MT and the age of the
Universe T0:
Here, G is the gravitational constant. Measuring R0 using the
distances and radial velocities of galaxies outside the virial radius of
the system Rvir, we can determine the total mass of the system
independent of its virial mass estimate. Note that both methods of
deriving mass from internal and from external galaxy motions
correspond to different linear scales where R0 is roughly four times as
large as the virial radius. In reality, galaxy groups and clusters do
not have perfect spherical symmetry, and the cosmology with =
0 is not true.
Numerous measurements of distances to nearby galaxies obtained
recently with the Hubble Space Telescope (HST) have allowed
us to investigate the Hubble flow around the Local Group (LG)
E-mail: (IDK); (OGN)
Nee Kashibadze.
and other proximate groups (Karachentsev et al. 2002, 2006, 2009;
Karachentsev & Kashibadze 2006). The radii R0 obtained from
observations for nearby groups around the Milky Way and Andromeda
(the LG), M81, Centaurus A, Maffei and IC 342, NGC 253 (Sculptor
filament) and NGC 4736 (Canes Venatici I cloud) are ranged within
0.71.4 Mpc. The average ratio of total-to-virial masses for these
six groups, derived from R0 using equation (1) and from Rvir, turns
out to be M T/Mvir = 0.60 0.15 (Karachentsev 2005). However,
as noticed by Peirani & Pacheco (2006, 2008) and Karachentsev
et al. (2007), in a flat universe dominated by dark energy the
resulting MT(R0) mass is higher than that derived from the canonical
LematreTolman equation (1). In the concordant cosmological
model with the term and m as a matter component, equation (1)
takes the form
MT = 8G2 R03 f 2H(02m) , (2)
f ( m) = (1
m (1
m)3/2arccosh
1 .
Assuming m = 0.24 and H0 = 72 km s1 Mpc1, which
corresponds to T0 = 13.7 Gyr (Spergel et al. 2007), we can rewrite
equation (2) as
= 2.12 1012
This yields a mass that is 1.5 times as large as that derived from
the classic equation (1). This correction leads to a good agreement,
on average, between the R0 mass estimates and the virial masses for
the above-mentioned galaxy groups.
For galaxies around the nearest cluster in Virgo, the expected
velocity deviations from the pure Hubble flow (the so-called
Virgocentric infall) were regarded in dynamical models by Hoffman,
Olson & Salpeter (1980), Tonry & Davis (1981) and Hoffman &
Salpeter (1982). These authors note that with the virial mass of the
Virgo cluster Mvir 6 1014 M , the radius of the zero-velocity
surface around the cluster amounts to 27 (i.e. the infall zone
covers nearly 1 steradian of the sky). According to Hoffman et al.
(1980), the observed decrease of radial velocity dispersion within
the angular distance = [024] from the Virgo centre for 228
galaxies agrees, in the main, with the Virgocentric infall pattern for
the cluster mass mentioned above. Tully & Shaya (1984) considered
the phenomenon of the infall of galaxies towards Virgo in both the
point-mass and distributed-mass models for the cluster with
different values of the cosmological parameter and the age of the
Universe T0. Using TullyFisher distance estimates for 19 galaxies
inside the virial radius of 6 and 14 galaxies outside it, the authors
ascertain the expected infall with R0 28.
Later, Tonry et al. (2000, 2001) developed a model of the
Virgocentric flow based on accurate distance measurements for 300 E
and S0 galaxies from surface brightness fluctuations. Their model
fits well with the observational data on galaxy distances and radial
velocities for the Virgo cluster distance of 17.0 Mpc and its total
mass of 7 1014 M . According to their model, our LG has a
peculiar velocity of 139 km s1 directed towards the Virgo centre.
Teerikorpi et al. (1992) and Ekholm et al. (1999, 2000) examined
the Virgocentric flow with different models of density distribution
in the cluster and inferred expected relations between velocities and
distances of galaxies relative to the cluster centre. Using Cepheid
distances to 23 galaxies and TullyFisher distances to 96 galaxies,
they concluded that the radius of the zero-velocity surface ranges
from 20 to 31, and the total cluster mass is equal to (12) of its
virial value.
During the last decade, the observational data base on distances
to galaxies in a wide vicinity of the Virgo cluster has grown
significantly, allowing us to determine R0 and, therefore, the total mass of
the Virgo cluster with better accuracy.
2 O B S E RVAT I O N A L S A M P L E S
To examine the phenomenon of the Virgocentric flow, we used
distance moduli of galaxies from different publications, preferring
more precise measurements. The main data sources are listed below.
(i) Taking the luminosity of the tip of the red giant branch
(TRGB) as a standard is the most efficient and the most universal
method to determine distances to nearby galaxies, as it is
practically independent of their morphological type. Being applied to
galaxy images in two or more photometric bands obtained with the
WFPC2 or ACS cameras on the HST, the TRGB method yields
an accuracy of distance measurements of 7 per cent, as found by
Rizzi et al. (2007). A consolidated list of distances for the Local
Volume galaxies is presented in the catalogue of neighbouring galaxies
(CNG; Karachentsev et al. 2004). The CNG sample of 451 galaxies
has been collected based on two conditions: galaxy distance D <
10 Mpc, if a galaxy has an individual distance estimate; otherwise,
galaxy radial velocity with respect to the LG VLG < 550 km s1.
Below, we use from the CNG the galaxies with only TRGB or
Cepheid distances, supplying these with new TRGB distances from
recent publications (Karachentsev et al. 2006; Tully et al. 2006).
(ii) The surface brightness fluctuation method (SBF), applying to
early-type galaxies, assumes that the old stellar population (RGB)
is prevailing in a total luminosity, and the galaxy structure does
not suffer from irregularities as a result of dust clouds. Using this
approach, Tonry et al. (2001) determined SBF distances to 300 E
and S0 galaxies with a typical errors of 12 per cent. This sample
is distributed over the whole sky extending to cz 4000 km s1
with a median velocity of 1800 km s1.
(iii) Mei et al. (2007) undertook a two-colour ACS/HST imaging
survey for 100 early-type galaxies situated in the Virgo cluster core
(the ACSVCS project). They derived precise SBF distances to 84 E,
S0 galaxies with a typical error of 8 per cent, and revealed the
threedimensional (3D) shape of the Virgo cluster to be a slightly triaxial
ellipsoid with axis ratios of (1 : 0.7 : 0.5). We expanded the ACSVCS
sample with other precise SBF and TRGB distance measurements in
the Virgo core made by Neilsen & Tsvetanov (2000) and Caldwell
(2006) with ACS/HST and by Jerjen, Binggeli & Barazza (2004)
with the Very Large Telescope. This yields the total ACSVCS+
sample of 116 galaxies.
(iv) In the wide vicinity of the Virgo cluster, there are 22
galaxies with distances measured by Tonry et al. (2003) using type Ia
supernovae (SNIa). This sample is small but has a distance error of
only 5 per cent.
(v) Based on the Two-Micron All-Sky Survey (2MASS)
Selected Flat Galaxy Catalogue (2MFGC; Mitronova et al. 2004),
Kashibadze (2008) determined distances to 402 spiral edge-on
galaxies with radial velocities <3000 km s1. A multiparametric
near-infrared TullyFisher relation was applied to these, yielding
a typical distance error of 20 per cent. The zero-point of the
luminositylinewidth relation was calibrated by 15 galaxies with
Cepheid and TRGB distance measures.
(vi) Finally, the former samples of galaxies were supplemented
with a compilation of distances by Tully et al. (2008, 2009), which
have been obtained from optical (B, R or I band) one-parametric
TullyFisher relations. This compilation relies on numerous H I
line and photometric observations carried out by Methewson
& Ford (1996), Haynes et al. (1999), Tully & Pierce (2000),
Koribalski et al. (2004), Springob et al. (2005), Theureau et al.
(2006) and other authors. Zero-points of the data were recalibrated
by a set of 40 galaxies with known Cepheid and TRGB distances.
As a last step, we used also distances from a very large and
important SFI++ sample (Springob et al. 2007), which have not been
included in the Tully et al. (2009) compilation. In total, we used
distance estimates for 941 spiral galaxies whose radial velocities
were limited by 3000 km s1. The typical distance error for these
is 20 per cent, although there are some cases with much higher
errors because of uncertainties of galaxy inclination, the presence
of interacting companions or H I profiles of low quality.
A substantial overlap between the two last luminositylinewidth
samples provides confirmation that their zero-points are the same,
and gives rms agreement per measure of 0.40 mag. As seen from
fig. 1 of Tully et al. (2008), there is an excellent agreement in
distance moduli between the luminositylinewidth and other (Cepheid,
TRGB, SBF and SNIa) measures. In particular, for 12 galaxies in
our list with both TF and TRGB or SNIa moduli, the mean distance
difference is (1.4 1.2) Mpc, while for 20 galaxies with SBF or
TRGB moduli the average difference is only (0.2 0.2) Mpc.
Following the previous authors (Tully & Shaya 1984; Ekholm
et al. 2000), we have formed a composite sample of galaxies limiting
their angular separation from the Virgo centre to < 30. We have
considered the radio galaxy Virgo A (NGC 4486) to be the physical
centre of the cluster as its position is close to the centre of X-ray
i: TRGB + Ceph
ii: SBF (Tonry)
iii: ACSVCS+
iv: SNIa (Tonry)
v: TF (IR)
vi: TF (opt)
emitting gas. The total number of galaxies in this cone volume with
apex angle < 30 is 630 the two-dimensional (2D) sample.
Limiting the angular separation of galaxies from the Virgo centre
introduces some selection effects into the Virgocentric flow
analysis. For this reason, we have also used another way to form the
observational sample, considering galaxies with spatial distances
from the Virgo cluster centre Rvc < 30 Mpc the 3D sample. This
approach suffers a drawback too because galaxy distances are
measured with errors and their significance is different at the proximate
and the distant boundary of the spherical volume (the so-called
Malmquist bias). The total number of galaxies in our 3D sample
amounts to 1792, and the fractions of diverse subsamples differ
significantly from that in the 2D sample.
Table 1 presents the summary of observational data that we have
used. The first column indicates the type of subsample, and the
second gives typical distance errors expressed in magnitudes. Columns
3 and 5 contain the numbers of galaxies in the cone (2D) or in the
spherical (3D) volumes. The sample goodness G, defined as G =
(N/100)1/2 m1, is a useful parameter that characterizes a statistical
weight of a certain sample (Kudrya et al. 2003). Goodness values
are indicated in columns 4 and 6. For example, the subsample of
galaxies with SNIa distances is scanty but its statistical significance
is comparable with that of other samples because of the higher
accuracy of distance measurements. As we can see, the galaxy
subsample ACSVCS+ has the maximum statistical weight in the 2D
set; however, almost all these galaxies are concentrated within the
virial radius. In the 3D set, the highest goodness corresponds to the
TRGB sample, but its majority is crowded on the nearby side of
the examined volume. The last two TF samples exhibit a significant
increase in number going from the 2D to the 3D samples, which is
caused by the well-known effect of morphological segregation of
late-type versus early-type galaxies along the cluster radius.
3 R A D I U S O F T H E Z E R O - V E L O C I T Y
S U R FAC E R0
The virial radius of the Virgo cluster Rvir = 1.8 Mpc (Hoffman et al.
1980) corresponds to its angular scale of 6.0, assuming the average
distance to the cluster members to be 17.0 Mpc. Radial velocities
and distances relative to the LG centroid for 259 galaxies in this zone
are represented in the top panel of Fig. 1. Here, precise distances
for most of the galaxies were obtained within the special survey
ACSVCS with the HST (Mei et al. 2007). The Virgo cluster
members, located in the distance range from 14 to 20 Mpc, demonstrate a
radial velocity scatter from 800 up to +2300 km s1. Foreground
galaxies are scarcely presented on the panel while background
objects tend to lie below the linear Hubble regression with the global
Hubble parameter H0 = 72 km s1 Mpc1 (Spergel et al. 2007),
showing thereby the expected effect of infall into the Virgo cluster
from the opposite side. The centroid of galaxies forming the virial
column at [17.0 1.8] Mpc, marked by vertical lines, has a mean
velocity +1004 70 km s1 versus the expected Hubble velocity
of +1224 km s1 at the distance of 17.0 Mpc. This can be explained
by a peculiar motion of the LG 220 70 km s1 directed
towards Virgo. The dotted and solid S-shaped curves correspond to
a Hubble flow perturbed by a point-like mass of 2.7 1014 and
8.9 1014 M (as the limiting cases discussed below) for the line
of sight passing exactly through the cluster centre.
The distributions of radial velocities and distances for the
remaining galaxies of the 2D sample in the close surroundings of Virgo
(6 < < 15) and in a distant periphery (15 < < 30) are
shown in the middle and bottom panels of Fig. 1. Here, the solid
and dotted S-shaped lines, having lower amplitudes, describe the
behaviour of the perturbed Hubble flow at angular distances equal
to 6 and 15, respectively. These panels display some signs of the
infall effect too; however, in front of Virgo, the expected infall is
barely seen.
Considering a set of such Hubble diagrams with their different
amplitudes of S-shaped waves decreasing with the angular distance
, we can find the quantity of the cluster mass that fits the observed
infall pattern in the best way. However, this approach seems to us
to be not transparent enough. In order to determine R0, and the total
cluster mass using this, we have converted our observational data
into distances and velocities expressed relative to the cluster centre.
The top panel of Fig. 2 shows the layout of a galaxy (G) relative to
the observer (LG) and the cluster centre (C) with angular separation
from the cluster centre. The spatial distance of the galaxy from
the centre therefore is
Rv2c = Rg2 + Rc2 2RgRc cos .
Assuming that the galaxy and the cluster centre are involved in
an almost unperturbed Hubble flow (the Hf case) with negligible
peculiar velocities, we can state the mutual velocity difference
between G and C in projection on to the straight line connecting them
as
where = + and tan = Rc sin /(R g Rc cos ).
The distribution of galaxies in the Virgocentric reference frame
{Vvc, Rvc} is represented in Fig. 3. Only the 391 galaxies with
angles obeying < 45 or > 135 from the whole 2D sample
are shown here. Selecting galaxies situated approximately in front
and behind the cluster is meant to reduce the role of tangential
velocity components, which are still unknown. The polygon curve
traces the running median with a window of 1 Mpc. The median
follows roughly the linear Hubble regression with H0 = 72 km s1
Mpc1 (the inclined dashed line) at middle Virgocentric distances of
15 Mpc, but tends to deviate from the H0 Rvc line at smaller scales,
crossing the zero-velocity line at R0 6 Mpc. The behaviour of the
running median at large scales is strongly skewed by a selection
effect because of the adopted limit for galaxy velocities VLG <
3000 km s1.
Another approach can also be used for converting the
observational radial velocity of a galaxy Vg into its Virgocentric velocity
(the case of pure Virgocentric flow; the Vf case). If the galaxy is
not involved in the general cosmological expansion but is falling
instead towards the Virgo cluster with a velocity Vin (Fig. 2b), then
its radial velocity relative to the observer will be expressed as
Vg = Vc cos
and the infall velocity Vin itself can be written as
Vin = (Vc cos
Figure 2. Galaxy (G) motion with respect to the cluster centre (C) in the
LG rest frame (top) in the case of almost pure Hubble flow and (bottom) in
the case of almost pure Virgocentric infall.
The angles and are shown in Fig. 2b. Evidently, the
discrepancy between these two extreme approaches, the Hf and Vf cases,
decreases when tends to 0 or to 180.
As can easily be seen, selecting galaxies in the cone both with
apex angle = 30 and with angle entails a loss of galaxies at
large Virgocentric distances. This becomes apparent in the top-right
corner of Fig. 3. A selection of galaxies in the volume Rvc < 30 Mpc
(3D sample) reduces the bias appreciably. Fig. 4 represents the sky
distribution of galaxies with known Virgocentric distances up to
30 Mpc in equatorial coordinates. The galaxies of this 3D sample
are marked as circles and their diameters indicate three distance
ranges: 012, 1222 and more than 22 Mpc from the observer. This
map shows that the selection of galaxies by their angle < 30
brings some systematic skews dependent on distance. In particular,
the foreground Virgo galaxies are preferentially removed by this
angular selection.
The Hubble diagram for 1792 galaxies of the 3D sample is
represented in Fig. 5. The symbols for objects from different sources of
distance data are the same as for Fig. 1. The number of galaxies in
the 3D sample is roughly three times as large as in the 2D sample.
It is worth noting that they populate the crucial regions in front and
behind the Virgo cluster more thoroughly, giving us an opportunity
for more detailed analyses of the Virgocentric infall. The velocity
distance relation for these galaxies with respect to the cluster centre
is shown in Fig. 6. The top panel corresponds to the assumption of
pure Hubble flow of galaxies (the Hf case) while the bottom panel
represents the case of pure radial motions towards the Virgo centre
(the Vf case). As previously, the galaxies located far away from
the line of sight crossing the cluster centre (i.e. with 45 < <
135) are eliminated in order to reduce the role of unknown
tangential velocity components. This condition diminishes the number of
sampled galaxies by 42 per cent.
A comparison of the top and bottom panels of Fig. 6 shows that
switching from the Hf case to the Vf case does not lead to any
dramatic changes in the Hubble flow pattern given in the Virgocentric
coordinates. Some galaxies move along the vertical axis
appreciably but the total behaviour of the running medians traces the infall
of galaxies towards the cluster in a similar way. The asymptotic
tendency of the median at large distances Rvc looks much more regular
for the 3D sample than for the 2D sample.
Our elimination of galaxies with 45 < < 135 is slightly
arbitrary. To estimate the response of the Virgocentric flow
pattern to changing this condition, we have also imposed a more rigid
constraint, eliminating galaxies with 30 < < 150. The
corresponding diagrams for the Hf and Vf cases are represented in Fig. 7.
As is seen, the more severe selection of galaxies by reduces their
number by more than a half. However, the behaviour of the running
median is almost the same.
In the bottom panel of Fig. 7, every galaxy from samples iiv
(see Table 1) having a distance error within 12 per cent is supplied
by error bars indicating where the galaxy should be situated if its
distance from the observer changes by 1 D. As expected, these
error bars are much longer for galaxies situated behind the cluster.
Changing a galaxy distance by 12 per cent, in some regions of the
{Vvc, Rvc} diagram, leads to significant displacement of the galaxy
along both Virgocentric coordinates, and therefore to appreciable
galaxy skips relative to the zero-velocity line. (We do not include
the longer error bars for the TullyFisher distances.)
To quantify the uncertainties on the running median curves
plotted in Figs 6 and 7, we generated extensive sets of bootstrap
realizations. Their results permit us to estimate the radius of the
zero-velocity surface and also its rms error presented in Table 2.
Column 1 shows the size of the window for a running median,
taken to be 0.8, 1.0 and 1.2 Mpc. Columns 2 and 3 show the mean
radius of the zero-velocity surface R0 and its rms scatter obtained
with regards to the assumptions on the pure Hubble flow (Hf case)
and the pure Virgocentric flow (Vf case), respectively; here only
four samples (iiv) with precise distance moduli were taken into
account. Columns 4 and 5 show the same quantities for samples
v and vi with TullyFisher distances. Columns 6 and 7 show the
radii R0 and their errors for the total set of available data on galaxy
distances. We discuss the interpretation of these different estimates
of R0 in the next section.
4 D I S C U S S I O N A N D C O N C L U S I O N S
We have analysed the available observational data on distances and
radial velocities of galaxies in the wide surroundings of the Virgo
cluster in order to study the Virgocentric infall. The main purpose of
this paper is to determine the radius of the zero-velocity surface R0,
which separates the cluster from the global cosmic expansion. By
using this observational quantity, we are able to estimate the total
mass of the Virgo cluster concentrated within R0 and compare it
with the virial mass estimates corresponding roughly to a four times
lower scale, Rvir. Based on the Hubble diagrams transformed into
Virgocentric coordinates and the results of our bootstrap numerical
experiments given in Table 2, we derive R0 to be in the range of
5.07.5 Mpc with a typical random error of 1.0 Mpc. The derived
value of R0 can be affected by some systematic circumstances.
The analysis of the Hubble diagrams in the Virgocentric
coordinates suffers from a lack of data on the tangential velocity
components of the galaxies. We tried to overcome this drawback with
assumptions regarding a dominant type of galaxy motion in the
proximity of Virgo. We performed a conversion of the observed
radial velocities of galaxies into their Virgocentric velocities under
two extreme kinematic assumptions: almost unperturbed Hubble
flow (the Hf case) or almost pure radial flow towards Virgo (the Vf
case). We found that adopting one or another scheme does not
significantly change the general pattern of the Virgocentric infall.
Calculating velocities in the Vf case yields, on average, some smaller
values of Vvc, which causes a slightly larger (+0.7 Mpc) value
of R0.
The R0 quantities presented in Table 2 tend to be correlated with
the smoothing window size. When the window changes from 0.8 to
1.2 Mpc, the radius decreases to 0.3 Mpc on average. Variation the
window size in a wider range, from 0.5 to 2.0 Mpc, still leaves R0
within its random errors.
The most noticeable systematic variations in the radius R0 are
seen in dependence on galaxy samples. The use of samples of
galaxies with only precise distance measurements (via Cepheids,
TRGB, SBF and SNIa) yields the radius R0 within 6.57.5 Mpc,
while the use of less precise TullyFisher distances leads to R0
estimates around 5.2 Mpc. The physical origin of this difference is
clear. Probably, the instance is related to the fact that a typical
distance error for the TullyFisher method (20 per cent) corresponds
at the Virgo distance to a linear scale of 3.4 Mpc, comparable with
the virial diameter of the cluster (3.6 Mpc). Large random errors
can throw galaxies over the virial column, diluting the shape of the
S-wave infall. Nevertheless, we should stress that two completely
independent sets of observational data on distances to early-type
Window (Mpc) 0.8 1.0
Primary distances
(samples iiv)
Hf
6.791.12
6.591.05
6.461.01
Vf
7.781.13
7.541.03
7.420.97
Hf Vf
5.071.04
4.870.88
4.710.78
5.581.13
5.380.97
5.240.87
All
Hf
5.150.96
5.001.00
4.800.95
Vf
5.821.04
5.651.07
5.521.03
and late-type galaxies lead to compatible values of R0. As can be
seen from Table 1, two samples with TullyFisher distances (v and
vi) are about two times as large in galaxy number as the samples
(iiv) with precise distances. Because we estimate R0 based on the
running median without regard to galaxy weights (distance errors),
the radius R0 for the total sample turns out to be closer to that for
the former samples.
Assuming R0 for the Virgo cluster in the range of (5.07.5) Mpc,
we obtain from equation (4) the total mass of the cluster to be
within MT = (2.78.9) 1014 M . This value is consistent with the
virial mass estimates for the Virgo cluster: (5.5 1.4) 1014 M
(Hoffman et al. 1980), (7.5 1.5) 1014 M (Tully & Shaya
1984) and 7.0 1014 M (Tonry et al. 2000) normalized to the
same Hubble parameter H0 = 72 km s1 Mpc1. It should be
remembered that this agreement is on very different scales as the
zero-velocity radius, R0, is roughly four times as large as the virial
radius. This means our results are consistent with there being no
additional mass outside the virial radius of the Virgo cluster.
Two items are worth mentioning in conclusion. The stated
method of estimating the R0 value from observational data relies
on the assumptions that a cluster has spherically symmetric shape
and that galaxy motions around the cluster are regular without a
significant tangential component. Deviations from the simple
spherical infall scenario have been considered both theoretically and
observationally by many authors (Peebles 1980; Davis & Peebles
1983; Lilje, Yahil & Jones 1986; Mould et al. 2000; Tonry et al.
2000; Watkins, Feldman & Hudson 2009). In particular, Tonry et al.
(2000) studied a peculiar velocity field around the LG and the Virgo
cluster in the presence of a second attractor (Great Attractor)
situated in HydraCentaurus. As seen from their figs 20 and 21, the
Great Attractor with a total mass of 9 1015 M , situated at a
distance of 43 Mpc, generates significant distortions in the velocity
field over an area of 1 steradian. Besides, Tully (1988) found the
so-called effect of Local Velocity Anomaly arising by a push of
the Local Void. According to Tully et al. (2009), a bulk motion of
260 km s1 toward the Supergalactic pole may be attributed to the
Local Void. Recently, cosmic velocity flows in the Local Universe
were also studied by Erdogdu et al. (2006), Haugbolle et al. (2007)
and Lavaux (2009).
We would emphasize that observational abilities to determine R0
and MT with better accuracy have not yet been exhausted. With the
derived R0 around 7 Mpc, the zero-velocity surface is situated at
a distance of about 10 Mpc from the observer (i.e. on the Local
Volume edge). Hence, we can expect to find some number of LV
galaxies with radial velocities (10002000) km s1, residing in
front of Virgo. A new updated version of the CNG (Karachentsev
et al., in preparation) contains about 40 candidate dwarf galaxies,
such as VCC1675, with appropriate radial velocities and rough
distance estimates. Their precise distances could be easily measured
using the TRGB with the facilities of the ACS on the HST in the
one-object-per-one-orbit mode. The addition of more galaxies with
measured distances in the range 911 Mpc from the LG would allow
a better measurement of R0. In particular, these galaxies could be
used to better rule out the case where there is a large amount of
mass outside the virial radius.
This work was supported by RFBR 07-02-00005, RFBR-DFG
0602-04017 and CNRS grants. The authors thank Dmitry Makarov,
Helene Courtois and Stefan Gottloeber for useful discussions. We
would also like to thank the anonymous referees for their valuable
comments, which led to significant improvements in the paper.